2m^2+10m+4=0

Solution for 2m^2+10m+4=0 equation:

Simplifying
2m2 + 10m + 4 = 0

Reorder the terms:
4 + 10m + 2m2 = 0

Solving
4 + 10m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 5m + m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 5m + m2)' equal to zero and attempt to solve:

Simplifying
2 + 5m + m2 = 0

Solving
2 + 5m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5m + -2 + m2 = 0 + -2

Reorder the terms:
2 + -2 + 5m + m2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5m + m2 = 0 + -2
5m + m2 = 0 + -2

Combine like terms: 0 + -2 = -2
5m + m2 = -2

The m term is 5m.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5m + 6.25 + m2 = -2 + 6.25

Reorder the terms:
6.25 + 5m + m2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + 5m + m2 = 4.25

Factor a perfect square on the left side:
(m + 2.5)(m + 2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(m + 2.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
m + 2.5 = 2.061552813

Simplifying
m + 2.5 = 2.061552813

Reorder the terms:
2.5 + m = 2.061552813

Solving
2.5 + m = 2.061552813

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = 2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = 2.061552813 + -2.5
m = 2.061552813 + -2.5

Combine like terms: 2.061552813 + -2.5 = -0.438447187
m = -0.438447187

Simplifying
m = -0.438447187

Subproblem 2
m + 2.5 = -2.061552813

Simplifying
m + 2.5 = -2.061552813

Reorder the terms:
2.5 + m = -2.061552813

Solving
2.5 + m = -2.061552813

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = -2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = -2.061552813 + -2.5
m = -2.061552813 + -2.5

Combine like terms: -2.061552813 + -2.5 = -4.561552813
m = -4.561552813

Simplifying
m = -4.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.438447187, -4.561552813}
Solution
m = {-0.438447187, -4.561552813}